Well a full introduction of the car would be nice. Pics would be spectacular but... whatever.
Turbo timers or idling a while before shutting down is really reserved for hard hard driving. Now most of us do some hard driving but spend a few minutes, if not more, completely off boost driving through traffic to our driveways or destinations. That really is more than ample to cool down a turbo.
If, However, you are at the track and have been pulling hard and spooling hard, then in an instant, are stopped in the pit or are done your heat, It's a good idea to let it idle a few minutes.
Edited to add: Aftermarket parts like what exactly? I would, since you just got it, enjoy it. Feel out how ridiculously floppy the rear end is with stock power. Master the rear end with stock boost.... then add power.